A representative passenger car that is designed for fuel economy has a frontal area of 2.6 m^2, drag coefficient of 0.3, rolling resistance coefficient of 0.01, curb weight of 1200 kg, maximum tractive force at low speeds of 3000 N, and tractive power at maximum speed of 30 kW. The vehicle has

Question

A representative passenger car that is designed for fuel economy has a frontal area of 2.6 m^2, drag coefficient of 0.3, rolling resistance coefficient of 0.01, curb weight of 1200 kg, maximum tractive force at low speeds of 3000 N, and tractive power at maximum speed of 30 kW. The vehicle has five-passenger capacity, plus rear end space behind the second seat for storage. Calculate the cruising power requirement at 96 km/h; the maximum speed; and the maximum gradability. (In standard units, the vehicle has a cross-sectional area of 28.1 ft^2, weighs 2640 lb, and the desired cruising speed is 60 mph.)

Accepted Answer

Assume air density of 1 kg/m[latex]^3[/latex]. The cruising speed is equivalent to 26.7 m/s. Therefore, using Eq. (13-1), the power requirement is

[latex]P_{\mathrm{TR}}=0.5 ho A_{F} C_{D} V^{3}+m g V C_{o}[/latex] (13-1)

P[latex]_{TR}[/latex]= 0.5(1)(2.6)(0.3)(26.7)[latex]^3[/latex] + (1200)(9.8)(26.7)(0.01) = 10.5 kW

Next, the tractive power at maximum speed of 30 kW will determine the maximum speed V[latex]_{max}[/latex]. Plugging in known values gives

[latex]30 \mathrm{~kW}=0.5(1)(2.6)(0.3) V_{\max }^{3}+(1200)(9.8) V_{\max }(0.01)[/latex]

Solving using a numerical solver gives V[latex]_{max}[/latex] = 40.2 m/s, or 145 km/h (90.4 mph).

Maximum gradability is determined using the maximum tractive force at low speed and the mass of the vehicle:

[latex]G R_{\max }=100 imes\left[\frac{3000}{\sqrt{(1200 \cdot 9.8)^{2}-(3000)^{2}}} ight]=0.264=26.4 \%[/latex]

Question 13.1: A representative passenger car that is designed for fuel eco...

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